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Ikard et al 2013a

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  1. 1. Case Study/ Characterization of Focused Seepage Through an Earthll Dam Using Geoelectrical Methods by S. J. Ikard1 , A. Revil2,3 , M. Schmutz4 , M. Karaoulis5 , A. Jardani6 , and M. Mooney7 Abstract Resistivity and self-potential tomography can be used to investigate anomalous seepage inside heterogeneous earthen dams. The self-potential (SP) signals provide a unique signature to groundwater ow because the source current density responsible for the SP signals is proportional to the Darcy velocity. The distribution of the SP signals is also inuenced by the distribution of the resistivity; therefore, resistivity and SP need to be used in concert to elucidate groundwater ow pathways. In this study, a survey is conducted at a small earthen dam in Colorado where anomalous seepage is observed on the downstream face at the dam toe. The data reveal SP and direct current resistivity anomalies that are used to delineate three anomalous seepage zones within the dam and to estimate the source of the localized seepage discharge. The SP data are inverted in two dimensions using the resistivity distribution to determine the distribution of the Darcy velocity responsible for the observed seepage. The inverted Darcy velocity agrees with an estimation of the Darcy velocity from the hydraulic conductivity obtained from a slug test and the observed head gradient. Introduction Earthen dams are designed to allow a limited amount of uniform seepage through their cores and foundations. When seepage exceeds than what is permitted, internal erosion may occur and increase locally the permeability of preferential owpaths. As the permeability is increased through erosion of ner particles, the hydraulics of seepage zones will also change over time. This can 1 Department of Geophysics, Colorado School of Mines, Green Center, Golden, CO; [email protected] 2 ISTerre, CNRS, UMR CNRS 5275, Universite de Savoie, Le Bourget du Lac, France. 3Corresponding author: Department of Geophysics, Colorado School of Mines, Green Center, Golden, CO; [email protected] 4 EA 4592, Institut Polytechnique de Bordeaux, 1 allee Daguin, Pessac, France; [email protected]l.com 5Department of Geophysics, Colorado School of Mines, Green Center, Golden, CO. 6Morphodynamique Continentale et Coti`ere, M2C, UMR CNRS 6143, Universite de Rouen, Mont Saint Aignan, France; [email protected] 7Department of Civil & Environmental Engineering, Colorado School of Mines, Golden, CO, [email protected] Received June 2013, accepted November 2013. 2013,NationalGroundWaterAssociation. doi: 10.1111/gwat.12151 lead to the formation of piping through the dam and the development of subsurface voids, both of which can cause sinkholes on the crest or side-slopes (Fell et al. 2003; Bendahmane et al. 2008). The occurrence of such localized seepages zones may therefore result in the sudden failure of an earthen dam (Foster et al. 2002; Fell et al. 2003). These processes are responsible for the second cause of catastrophic failures for earthen dams, for about 46 % of all documented failures (Foster et al. 2000, 2002; Fell et al. 2003; Wan and Fell 2004). The highly uncertain outcomes and timescales over which seepage zones can evolve to threaten the safety condition of an earthen dam mandate a need for improved methodologies that allow for (1) noninvasive detection capabilities with improved resolution over broad and compact spatial scales, (2) rapid deployment and detection capabilities so that the geometrical evolution of seepage zones can be monitored in real time, and (3) the ability to provide quantitative estimates of seepage-related hydraulic parameters in real time with improved accuracy. Our goal in this study is to take advantage of some recent developments in self-potential tomography (SPT) (Soueid Ahmed et al. 2013), in order to detect preferential owpaths in earthen dams. The self-potential (SP) method NGWA.org Groundwater 1
  2. 2. is a passive geophysical method sensitive to groundwater ow (Sill 1983; Rozycki et al. 2006; Bol`eve et al. 2009, 2011). Indeed, the source current density responsible for the occurrence of SP signals is directly proportional to the Darcy velocity. However, the subsurface distribution of electric resistivity must also be known in order to interpret SP signals (Jardani et al. 2007). To our knowledge, SP and resistivity data are rarely used in concert to localized concentrated seepage in earth dams. In this study, we apply the SP and direct current (DC) resistivity methods to a small leaking earthen dam in Colorado at which focused seepage has been observed on the downstream toe. Description of the Geophysical Methods Electrical Resistivity Tomography DC resistivity method is an active geophysical method that employs specic geometrical congurations of electrode arrays to inject very low-frequency currents into the subsurface and measure a voltage drop response at a set of electrodes. The ratio of the measured voltage drop by the imposed electrical current, corrected for the geometry of the array, corresponds to an apparent resistivity. A pseudosection corresponds to a collection of apparent resistivity measurements (Grifths and Barker 1993). The pseudosection can be inverted in either two dimensions (2D) or three dimensions (3D) to produce an electrical resistivity tomogram (e.g., Loke and Barker 1996) that displays an estimate of the true subsurface resistivity distribution. This approach is called electrical resistivity tomography (ERT) and has been broadly used in hydrogeophysics. The inverse of the resistivity, the electrical con- ductivity, is related to two fundamental properties of the porous soils and rocks, namely the connected porosity and the cation exchange capacity CEC (Revil 2013a, 2013b): = 1 F w + S (1) S 1 F S(+) (1 f ) CEC (2) where w (in S/m) corresponds to the pore water con- ductivity, S (in S/m) denotes the electrical conductivity associated with the electromigration of the cations in the diffuse layer coating the surface of the grains (see Figure 1a and 1b), F (dimensionless) is the formation factor related to the porosity by Archies law (F = m , Archie 1942, m is called the cementation exponent or rst Archie exponent and is typically in the 1.5 to 2.5 range), S (in kg/m) denotes the mass density of the solid phase (typically 2650 kg/m3 for silicates), (+) (m2 /s/V) corresponds to the mobility of the counterions in the diffuse layer, the external part of the electrical dou- ble layer (see Figure 1b) ((+)(Na+ , 25 C) = 5.2108 m2 /s/V), f (0.90) denotes the fraction of counterions in the Stern layer (the inner part of the electrical dou- ble layer), and CEC denotes the CEC (in C/kg) of the material. The ERT method has been extensively used on dams to determine the subsurface architecture of earthen dams and to perform monitoring of changes in porosity (Nasser 1994; Panthulu et al. 2001; Cho and Yoem 2007; Sjodahl et al. 2006; Blome et al. 2011). An electrically conductive pathway can be conductive because of the high porosity of the material or because of the presence of clay with a high CEC and therefore a low permeability (Revil and Cathles 1999). Therefore, ERT is sensitive to the presence of conductive pore uids but is not a ow indicator, and therefore, any interpretation should be carefully analyzed and informed with additional geophysical and hydraulic data. As discussed in the following section, the SP method is naturally a complementary method to ERT. The SP Method The SP method is a passive geophysical technique directly sensitive to groundwater ow (e.g., Ikard et al. 2012; Revil et al. 2012). It has been extensively used qualitatively to investigate preferential groundwater ow pathways in dams and embankments (Ogilvy et al. 1969; Corwin 1985; Butler et al. 1989; Butler et al. 1990; Alsaigh et al. 1994; Panthulu et al. 2001; Minsley et al. 2011) and more recently quantitatively (Bol`eve et al. 2007a, 2009, 2011; Moore et al. 2011; Bol`eve et al. 2012). Recent algorithms have been indeed developed to invert SP data in order to localize preferential owpaths using cross-correlation (Rozycki et al. 2006) and stochastic methods (Ikard et al. 2012) and to estimate the groundwater ow pattern and Darcy velocity using deterministic inversion algorithms (Bol`eve et al. 2009, 2011). A SP mapping survey is simple to perform and requires only a voltmeter characterized by a high internal impedance (>10 M ), a cable reel, and two nonpolariz- ing electrodes to passively measure naturally occurring voltages. The occurrence of SP signals associated with ground- water ow originates at the pore scale. The pore water inside of a porous material is never electrically neutral. There is usually an excess of charge in order to com- pensate for the deciency of electrical charges on the mineral surface at the pore walls (Overbeek 1952, see Figures 1a and 1b). The ow of the pore water is respon- sible for the advective drag of this excess of electrical charges (Figure 1c). This advective current density (ow of charges per unit surface area of a cross section of the porous material and per unit time) is called the stream- ing current density in the literature (Overbeek 1952; Sill 1983; Levenston et al. 1999). Revil and colleagues developed a new formulation of the streaming current density that is valid for any pore size (Jardani et al. 2007; Revil and Mahardika 2013). In this formulation, the source current density is associated 2 S. J. Ikard et al. Groundwater NGWA.org
  3. 3. L R zr OMineralsurface X M+ M+ M+ M+ Sternlayer OHP Shear plane M+ M+ A M+ M+ o-Plane d-Plane M+ A A A M+ M+ M+ BulkporesolutionM+ M + X X X X X X X X X M+ M+ Sketch of a charged capillary Sketch of the electrical double layer Source current density Mineral Mineral Pore Mineral Flow (a) (b) (c) Figure 1. Description of the electrical double layer and the streaming current density. (a) Sketch of a single capillary of radius R coated by the electrical double layer. (b) Sketch of the electrical double layer showing the Stern layer of sorbed counterions and the diffusion layer; M+ denotes the metal cations while A denotes the anions. The charge of the diffuse and Stern layer counterbalances the charge on the mineral surface. A consequence of the electrical double layer is the existence of an excess of electrical charge in the pore water, located in the vicinity of the mineral surface. The o-plane refers to the mineral surface and the d-plane to the interface between the Stern layer and the diffuse layer. (c) The ow of water through the pore network drags this excess of charge generating a streaming current density (modied from Revil et al. 2011). with the drag of the effective excess of charge QV caused by the ow of the pore water and is therefore given by jS = QVu (3) where u (in m/s) denotes the Darcy velocity and QV (in C/m3 ) denotes the excess of electrical charge that is carried along with the ow of the pore water. For pH comprised between 5 and 8, Jardani et al. (2007) found that the QV is controlled by the permeability k (in m2 ) and they developed the following empirical relationship: log10 QV = 9.2 0.82 log10 k. (4) Equation 4 holds for a broad range of porous rocks and soils (see also an updated data set in Revil and Mahardika 2013). In conductive materials, the source current density jS is responsible for an electrical eld and the tangen- tial component of this electrical eld is measured at the ground surface (e.g., Revil et al. 2012). A classical mistake is to mix the local potentials in the elec- trical double layer coating the surface of the grains with the macroscopic eld that is measured in SP studies. These physical quantities are unrelated to one another. With respect to the macroscopic electrical eld, the generalized Ohms law for the total current density j is written as j = E + jS (5) where denotes the electrical conductivity of the porous material. Equation 5 is combined with a conservation equation for the electrical charge that is written as (Sill 1983) j = 0 (6) The combination of Equations. 5 and 6 yields the following elliptic partial differential equation for the NGWA.org S. J. Ikard et al. Groundwater 3
  4. 4. SP (in V) (Sill 1983): () = jS (7) The right-hand side of Equation 7 corresponds to the SP source term associated with the Darcy velocity distribution and the heterogeneity in the distribution of the volumetric charge density. In terms of laboratory measurements, the magnitude of the SP signals can be estimated from the streaming potential coupling coefcient. This coefcient is quanti- ed as follows. We rst express Darcys law in a saturated porous media as u = Kh, where h (m) denotes the hydraulic head and K (m/s) the hydraulic conductivity (Darcy 1856). The streaming potential coupling coef- cient C (in V/m) is dened as the variation of the SP for a variation of the hydraulic head h when ow is allowed through a core sample and the end-faces are not short-circuited. C is given by C h j=0 = QVK (8) where = 1/ denotes the electrical resistivity of the porous material (in m). We will see in the following how this coefcient can be measured in the laboratory (Bol`eve et al. 2007b; Malama and Revil 2013). Forward modeling of the SP signals associated with groundwater ow was pioneered by Sill (1983). Figure 2 shows the 2D forward modeling of the SP signals associated with the existence of a preferential seepage in an earthen dam (hydraulic conductivity K = 106 m/s) with granular sand-silt materials (K = 105 m/s) and with a clay core (K = 109 m/s). We see the presence of a negative anomaly upstream and the presence of a positive anomaly downstream at the dam toe. The amplitude of these SP anomalies is controlled both by the conductivity of the pore water (fresh water implies higher SP anomalies) and by the head gradient. We propose the use of SPT, a method recently proposed initially by Jardani et al. (2007), to use SP signals to determine the owpath of an observed seepage in a small dam in Colorado. The algorithm that will be used for the inversion of the SP data is described in the next section. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 2 4 6 8 10 12 14 16 18 20 22 24 28 28 0 2 4 6 8 10 Re (0 mV)fElevation (m) 8 1410 12 16 18 20 22 24 26 28 6 4 2 0 2 4 6 8 10 Self-potential(mV) . Ref Distance (m) Modeled self-potential Lake Water saturation Clay core 1 mV 2 mV 4 mV 7 mV 7 mV 4 mV -1 mV -4 mV Flow path Distance (m) Figure 2. Example of SP modeling on an earthen dam with a clay core. We have created a owpath with an increased permeability channeling water through the clay core. The groundwater ow is used to simulate the SP signals. The SP signals are collected at the ground surface to create the SP prole (adapted from Bol`eve et al. 2009). Note that the position of the positive SP anomaly coincides with the seepage area. Computation performed with the nite-element package Comsol Multiphysics 3.5. 4 S. J. Ikard et al. Groundwater NGWA.org
  5. 5. Self-Potential Tomography With the nite-element method, Equation 7 can be written in matrix form as (Soueid Ahmed et al. 2013) dp = Km (9) where dp represents the predicted SP data at a set of stations, m represents the vector of current density (for each cell and in 2D, the current density has two components), and K is called the kernel and corresponds to the Greens functions of the problem, which accounts for the resistivity distribution. An extensive discussion about the computation of the kernel for the source current density is given by Jardani et al. (2008), and more recently, a free software has been developed by Soueid Ahmed et al. (2013). An important point is that the kernel cannot be computed correctly without the knowledge of the resistivity distribution. Therefore, ERT is an important ingredient of SPT. The inversion of the SP signal recorded at the ground surface involves a reconstruction of the spatial distribution of the amplitude and direction of the source current density vector m given a set of observed data do (N -vector of observed SP data). Deterministic inversion with Tikhonov regularization is used, considering the minimization of an objective function, which is the sum of at least two terms. The rst term is the data mist function for which the difference (according to a given norm, usually the L2 norm) between the predicted and observed data should be minimized. However, for potential eld problems, the solution of the inverse problem is highly nonunique and many models can reproduce the data equally well. Therefore, a regularizer is added to the cost function. The idea is to use a groundwater ow model (set up with a minimum of constraints, for example, ow in a homogeneous material with the correct topography and the correct boundary conditions) as prior model (denoted as m0). The idea is to start the inversion from this model and to perturb iteratively this prior model using the SP data as additional constraints. The objective function to minimize, P (m), is dened as P (m) = Wd (Km do) 2 2 + 2 W m (m m0) 2 2 (10) where do denotes the vector of observed SP data, the subscript 2 corresponds to the L2 norm, the regular- ization parameter that is incorporated with the constraint 0 < < , and m = Jx s , Jz s corresponds to the model vector with the two components of the source current density (x and z components). The model vector has there- fore 2M components (M is the number of cells used to discretize the subsurface) and the kernel matrix K has N 2M components Kij = Kx ij , Kz ij . In Equation 10, the matrix Wd = diag{1/ 1, . . . , 1/ N } denotes a diagonal weighting square (N N ) matrix. Elements along the diagonal of Wd correspond to the reciprocal of the standard deviation squared. The matrix W m = 2 mI denotes the weighting diagonal matrix that represents the weight of the a priori model used in the minimization controlled iteratively from the regularization parameter. The minimization of the objective function P (m)/m = 0 is conducted with the Gauss-Newton algorithm implemented in Matlab (see Richards et al. 2010 and Soueid Ahmed et al. 2013). The program was initiated with a prior model and = 1, which reduces at each iteration to half of the value at the previous iteration. After the third iteration, the SP data are reproduced with a small RMS error of 0.12%. The current density vector is translated into Darcy velocity using the linear relationship between current density and Darcy velocity u = jS/QV for the value of QV that determined from laboratory tests to quantify the coupling coefcient. Description of the Test Site Localization and Geometry The eld site is an earthll dam (no clay core; properties described in next section) that impounds a small reservoir in the Rocky Mountains near Avon, Colorado. The reservoir is anked by the steep, brushy sub-alpine side-slopes of the drainage gulch and collects surface and groundwater from a 7.8 km2 drainage basin. It has a normal storage capacity of 24,670 m3. The reservoir surface area is approximately 8094 m2 at the maximum storage elevation of 2411 masl (meters above sea level), and the maximum reservoir depth is 5.8 m at full capacity. The dam has a structural height of 11 m (referenced to the downstream dam toe), a hydraulic height of 10 m, and 1 m of freeboard elevation between the emergency spillway S1 and embankment crest at the maximum pool elevation (Figure 3b). The dam is 37 m wide at the base and is 4.9 m wide at the crest. The crest is at an elevation of 2412 masl and spans 122 m in length between the side-slopes of the drainage gulch. The upstream slope of the embankment is lined with rip- rap on a 2:1 slope (horizontal:vertical) to an elevation of 2409 masl and has 3:1 grade below. The downstream slope has a 2:1 grade to the toe at 2402 masl, where the downstream slope intersects the natural topography of the gulch. Portions of the downstream slope near the toe of the maximum cross section are signicantly steeper (as much as 1.6:1). The dam has two spillways. The primary spillway (see Spillway S1 in Figure 3b) is a 630-mm diameter corrugated metallic pipe through the west abutment into the reservoir. We have checked that the corrugated metallic pipe is responsible for a small negative SP anomaly that does not inuence the overall SP map discussed later. The emergency spillway (shown in Figure 3b as Spillway S2) on the east abutment is an open channel graded from 9 m wide at the concrete cutoff wall marking the spillway crest into a 3.7-m wide channel, approximately 26 m downstream. NGWA.org S. J. Ikard et al. Groundwater 5
  6. 6. Crest Reservoir at low level Spillway S1 Reservoir water gauge Picture of the test site 0 25 50 Meters Reservoir Ref. Inlet N P1 P3 P2 P4 P5 P1 1 P10 P8 P7 P6 P12 P9 P1 Position of the profiles (a) (b) Pz1 Spillway S2 S2 S1 Figure 3. Description of the test site. (a) Position of the DC resistivity and SP proles for the reconnaissance survey. Five DC resistivity proles (P1 to P5) were acquired parallel to the dam crest with a 2.5-m electrode spacing, and six proles (P6, P7, P8, and P10 to P12) were acquired perpendicular to the dam crest with a 1-m electrode spacing. One prole (P9) was collected oblique to the East abutment, perpendicular to a suspected seepage path through the abutment, with a 1-m electrode spacing. A total of 1049 SP stations were acquired along DC survey lines with a 1.25-m spacing parallel to the crest and a 1-m spacing perpendicular to the crest (Ref. denotes the position of the reference for the SP measurements). (b) Picture of the reservoir lake at low level with the position of the two spillways S1 and S2 and the crest of the earth dam. The overow pipe is also visible in the middle of the dam (see Reservoir water gauge). Properties of the Dam Materials Geotechnical properties and internal zoning of the dam are unknown. The few available inspection records and engineering reports (Blair 2003, 2004, 2010a, 2010b) have assumed that the dam is composed of homogeneous earthll resembling soils encountered in test pits exca- vated at the east abutment of the dam, due to the close proximity of the test pits to original 1936 borrow area. The State of Colorado assumes that the dam is homogeneous earthll composed of silty clay materials compacted to 95% maximum density during emplacement (Blair 2003, 2004, 2010a, 2010b), but this is unconrmed. Quantita- tive geotechnical data regarding the original construction materials and those used in historical modications are not available. Anomalous Seep A seep has been observed at the downstream toe of the maximum cross section of the dam (see seep area in Figure 4). During this study, visible water exiting the dam at the downstream toe (i.e., seep) was observed over a distance of few meters parallel to the dam crest approximately intersecting resistivity line P6 (see position in Figure 3a). The discharging seepage water ows continuously under the hydraulic load of the maximum reservoir storage behind the dam. Visual observations recorded by eld engineers and state regulators on several occasions over a period of 2 years have indicated that the seepage exiting the downstream toe is between 0.6 L/s and 1.9 L/s when the reservoir is at full capacity. Data Acquisition SP and DC resistivity surveys were completed in summer 2011 to identify the source of anomalous seepage emanating from the dam toe. The reservoir water level was held constant at the maximum storage level (2412 masl) throughout the survey. The seepage zone water was observed to be clear. The electrical conductivities of the reservoir water and seepage water were measured to be 308 S/cm and 440 S/cm (at a temperature of 8.7o C), respectively, using a conductimeter. Twelve DC resistivity proles were collected parallel and perpendicular to the dam covering the crest, spillways, downstream slope, and a portion of the downstream topog- raphy and side-slopes of the drainage gulch (Figure 3a). Resistivity measurements were acquired with an ABEM Terrameter SAS4000 using a Wenner array with 64 elec- trode separated by 2.5 m for proles parallel to the dam crest and separated by 1 m for proles perpendicular to the crest. The measured contact resistivity between the electrodes and the ground was less than 1 k . The resis- tivity measurements were repeated to achieve a standard deviation of the apparent resistivity that was less than 3% of the mean value. The resistivity proles along the upstream edge (P1) and downstream edge (P3) of the crest were separated by 5 m, and DC resistivity proles on the downstream slope parallel to the crest (P2, P4, P5) were separated by about 10 m (Figure 3a). The proles perpendicular to the crest (P6 to P12) had an average separation of 16 m. One additional prole (P9) was performed perpendicular to a suspected seepage path through the East abutment using 59 electrode takeouts and an electrode separation of 1 m. A total of 1049 SP stations were monitored along the DC resistivity proles with a handheld Fluke 289 volt- meter and two nonpolarizing Petiau Pb-PbCl2 electrodes (Petiau 2000). A reference Petiau electrode was buried in a shallow hole that was excavated above the reservoir on the east side-slope of the gulch (see position Ref in Figure 3a), and a roving Petiau electrode was used at each of the 1049 stations. All SP data were measured as the potential difference between the roving electrode and the reference electrode. The station separation for SP measurements was 1.25 m for proles parallel to the 6 S. J. Ikard et al. Groundwater NGWA.org
  7. 7. 16 20 15 10 5 0 5 10 15 20 0 8 16 24 32 40 48 56 Iteration 4, RMS 5% Crest Bedrock Profile P6 South P3P1 P2 P4 P5 Depth(inmeters)Self-potential(inmV) Position (in m) Aquifer September 2011 Water 0 2 4 6 8 10 12 14 Resistivity (in ohm m) 40 50 70 100 200 300 Seep A2 Path 2 Seep River North Vadose zone Figure 4. Example of 2D resistivity and SP prole normal to the dam structure (Prole P6, see position in Figure 1a). The grey area corresponds to the area where seepage A2 can be observed at the ground surface. This seepage is associated with a relative 20 mV positive SP anomaly with respect to the local minima on its anks (surrounding values). crest and 1 m for proles perpendicular and oblique to the crest. At each SP station, a shallow hole was exca- vated to expose moist soil and reduce contact resistance between the roving electrode and the ground. Stations on the crest and some stations perpendicular to the west abut- ment were watered with reservoir water to reduce contact resistance. The maximum contact resistance for all SP stations was 40 k and on average was less than 15 k , much smaller than the internal impedance of the volt- meter (100 M ). The potential difference was measured between the reference and roving Petiau electrodes before and after acquiring each 1049 station survey to correct for electrode drift. Telluric currents were assumed to be negligible due to the small, conned nature of the eld site and were not monitored. Some SP proles are shown in Figures 4 to 6 together with the resistivity proles. A SP map is shown in Figure 7. Electrical Resistivity Tomogram (ERT) The inversion of the apparent resistivity data was performed with RES2DINV (Loke and Barker 1996) with the nite-element approach and a Gauss-Newton algorithm. The 2D DC resistivity proles and the associated SP data are shown in Figures 4 to 6. Data quality was excellent due to a very good contact between the stainless steel electrodes and the ground (contact resistance generally < 1 k as discussed earlier). Five proles (P1 to P5) were also inverted in 3D with the software ERTLab (Morelli and Labrecque 1996, Santarato et al. 2011) using the nite-element method with tetrahedrons. The 3D inversion only incorporated the proles collected parallel to the dam crest, the proles normal to the dam were spaced too far apart to bring pertinent information. The whole data set for the 3D inversion was composed of 319 electrodes, 2357 quadripoles, and 323 topographic data points. The inversion converged in three iterations leading to a low RMS error of 5%. The topography was taken into account in the inversion. The mesh grid size was equal to 1.25 m in all directions. The result of the 3D tomography is shown in Figure 8. Interpretation of the Geophysical Data The resistivity proles show a shallow resistive layer (resistivity in the range 200 to 300 m) just below the ground surface, e.g., prole P6 in Figure 4. This layer NGWA.org S. J. Ikard et al. Groundwater 7
  8. 8. 30 20 10 0 10 20 0 50 100 150 Profile P2 Self-potential(inmV) Position (in m) September 2011 Spillway B Depth(inmeters) 10 5 0 5 10 15 20 25 30 Iteration 4, RMS 3.0% Bedrock Conductive body (Aquifer) Resistivity (in ohm m) 40 50 70 100 200 300 West East Figure 5. Example of 2D resistivity and SP prole parallel to the dam crest (Prole P2). The high density of measurement can be used to determine the standard deviation to be 3 mV. This prole shows the lateral zone of saturation associated with the aquifer. The SP signals are essentially uniform indicating a rather uniform seepage in the upper part of the dam. is interpreted as the vadose zone above the capillary fringe. This is consistent with the fact that the water table is approximately 1 to 2 m below the ground surface at piezometer Pz1 (see position in Figure 3a). The resistivity proles show areas of low-resistivity anomalies (on the order of 40 to 50 m, see Figures 4 to 6 and Figure 8). The conductivity of the pore water is w = 0.052 S/m (19 m resistivity, 529 S/cm) measured in the eld in piezometer Pz2 on July 9, 2012 (on July 9, 2012, the background conductivity in piezometer Pz1 was measured and was 549 S/cm). The referenced values were 440 S/cm and 308 S/cm August 9, 2011 during the reconnaissance survey. The porosity of the dam material is estimated to be around 0.30 (30%). This implies a formation factor F of about 11 (using a cementation exponent of 2.0 as default value, see Archie 1942). = 0.025 S/m (using 40 m from the resistivity tomogram) implies a surface conductivity S of 0.020 S/m. This is a rather high value indicating that the earth material could be clayey. We interpret the low- resistivity zones as areas of relatively high permeability and the value of the permeability will be discussed further. However, as mentioned earlier, great care should be taken in analyzing resistivity as it is inuenced by the clay content, the clay mineralogy, and porosity. The low-resistivity area below the crest (see Figure 5) is interpreted as a seepage zone of the groundwater that has entered the dam cross section from the reservoir. Beneath the crest, the phreatic surface is uniformly distributed in Prole P2 (see Figure 5), suggesting a uniform entry of reservoir water into the upstream slope of the dam. The seepage separates into preferential owpaths in a downstream direction as shown in Proles P2 and P5 parallel to the crest (Figure 6). Seepage starts to deviate from uniform into preferential channels in Prole P4 (not shown here) along the midsection of the downstream slope. In Prole P5 (Figure 6), we can clearly observe three localized channels in the dam shown by conductive anomalies (see also Figure 8 where these seepages are named Paths 1, 2, and 3). Flow through the central path appears to be the primary contribution to the observed seep at the downstream dam toe (see position of the seep in Figures 4 and 7). Indeed, the high-conductivity seepage Path 2 correlates at its termination with the position of the observed seep. SP data are complementary to the 2D/3D electrical resistivity tomograms in deciphering the position of the owpaths. The positive SP anomalies (15 to 30 mV with respect to the reference electrode) are observed downstream of the dam, in its central portion (see the 8 S. J. Ikard et al. Groundwater NGWA.org
  9. 9. 20 15 10 5 0 5 10 15 20 0 50 100 150 Profile P5 Self-potential(inmV) September 2011 Iteration 4, RMS 5.1% Depth(inmeters) 10 5 0 5 10 15 20 25 30 Bedrock Path 2 Spillway S2Spillway S1 Resistivity (in ohm m) 40 50 70 100 200 300 A1 Path 1 Path 3 Green vegetation Seep Position (in m)West East Figure 6. Example of 2D resistivity and SP prole parallel to the dam crest (Prole P5). The high density of measurement allows determining the value of the standard deviation (about 3 mV). This prole shows three well-developed owpaths named Path 1, Path 2, and Path 3. Path 2 is responsible for the observed seepage on the downstream toe of the dam. Its seepage is associated with a positive SP anomaly with respect to the background value. anomalies A1 and A2 in Figure 7). The maximum positive SP anomaly was observed in Prole P6 (see Figure 4). Note that both spillways were carrying water during the survey. The positive SP anomalies on the downstream slope of the dam are interpreted as zones of water upwelling in the vicinity of the ground surface (see for instance the simulation shown in Figure 2). The localization of these zones is consistent with the position of the preferential owpaths interpreted from the DC resistivity proles. A clear seep is only observed at the bottom of Prole P6 (see Figure 4). However, other indicators of seepage (for instance green and abundant vegetation) have been observed at some locations on the downstream slope that are consistent with positive SP anomalies (>10 mV with respect to the background, see for instance Figure 6). The location of anomaly A1 in Figure 7 has been consistently observed over several months to have signicantly greener vegetation with respect to surroundings. This area was noted to show increased soil moisture content with respect to surroundings and a sloshing sound when DC electrodes were installed in this location. Tall, dense vegetation and noxious weeds have been observed sprouting from the downstream slope at the location of A2 (Figure 7) during the summers of 2009 and 2010. A2 and A3 were also observed to have increased soil moisture (although not as signicant as A1) with respect to surroundings. Self-Potential Tomography The goal of this section is to show how the SP data along Prole P6 can be interpreted quantitatively to estimate the Darcy velocity. For this purpose, we rst determine the streaming potential coupling coefcient of a core sample from the dam and then we proceed to invert the SP data in terms of source current density distribution, which is then converted into a spatial distribution of Darcy velocity. Laboratory Investigation A sample of material representative of the aquifer shown in Figure 4 has been collected at a depth of 2 m with an auger. The sample was estimated to be predom- inantly silty clay through visual and textural analysis. It was representative of the texture and composition to the embankment ll materials described in the lithologic logs. The embankment ll materials is a disturbed version of NGWA.org S. J. Ikard et al. Groundwater 9
  10. 10. Area 1 Area 2 Elevation(m) 2415 2410 2405 4388300 4388280 4388260 4388240 4388220 Seep A1 A2A3 Self-potential map (with topography)(a) (b) Self-potential(inmV) 25 15 5 5 15 25 Easting (m)372000 372020 372040 372060 372080 Northing (m) Thresholded resistivity tomography Seep Seepage 1 Seepage 2 Seepage 3 Area 1 Area 2 Figure 7. SP and resistivity data. (a) SP map (total of 1049 SP stations). Negative SP anomalies on the abutments and downstream slope in the approximate range of 15 to 30 mV are a result of ow through preferential paths imaged in DC resistivity tomography. The positive SP anomalies in areas A1 to A3 may correspond to the upow of water as shown in Figure 2. Anomaly A2 indicates the potential for upow paths near the observed seepage zone. The areas A1 and A3 are characterized by very green vegetation. Seep corresponds to the position of the observed seep downstream the dam. (b) Threshold resistivity distribution showing the anomalies less than 50 m in magnitude. the soils excavated from on-site borrow areas, which have been reported to be silty clays, although no quantitative geotechnical data are available to conrm this assump- tion. The silty clay assumption, as well as the textural characteristics observed and recorded during the sample excavation, do justify the use of this high value. The hydraulically conductive nature of the sediments indicated by the slug test is in agreement with lithologic logs of piezometer installation. Boring logs for piezometers Pz1 and Pz2 were supplied by Hepworth-Pawlak Geotech- nical. Borings were drilled on July 28, 2004 using a track-mounted drill rig during a low pool storage condition in the reservoir. Unfortunately, geotechnical analysis of boring samples was not performed in a laboratory. Boring logs of Pz1 indicate that embankment ll was encountered between depths of 0 m and 11 m consisting of sandy grav- elly clay, scattered cobbles. The ll was medium stiff to very stiff, moist, and dark brown in color. Gravel was encountered below the embankment ll between depths of 11 and 15 m. The gravel was noted to be dense, sandy, and silty with cobbles and small boulders and was red in color. It was also noted to be moist with saturation increasing with depth. The water table was encountered at a depth of 15 m in Pz1 during installation. Pz1 is slot- ted between depths of 11.5 and 15 m. The lithologic log in Pz2 indicates that embankment ll was encountered between depths of 0 m and 4.6 m and has the same char- acteristics as those encountered in Pz1. The gravel layer encountered in Pz1 was also encountered in Pz2 between depths of 4.6 and 8.6 m. The water table was encoun- tered at a depth of 5.3 m during installation. Pz2 is slotted between 5 and 8.6 m. The logs show a more hydraulically conductive layer underneath the embankment ll. Our goal was to use this sample to get an estimate of the streaming potential coupling coefcient to connect the source current density to the Darcy velocity. The experi- mental setup used is shown in Figure 9a and the streaming potentials vs. hydraulic heads are shown in Figure 9b. Water from the reservoir was used for this experiment. The value of the streaming potential coupling coefcient is determined from the slope of the streaming potential vs. hydraulic head data, which is equal to 2.6 0.2 mV/m. We also measured the resistivity (40 m) and the perme- ability (k = 3.8 1012 m2 , corresponding to a hydraulic 10 S. J. Ikard et al. Groundwater NGWA.org
  11. 11. (a) (b) (c) Figure 8. 3D electrical resistivity tomogram from Proles P1 to P5 (2357 apparent resistivity data). (a) 3D inversion of the DC resistivity. (b, c) 2D plan view slices at different depths below the topography. Three potential seepage paths are shown within the dam, diverging from uniform ow in a downstream direction. One path is imaged through each abutment, and one path is imaged beneath the maximum cross section in the center of the dam. The central preferential owpath (Path #2) through the maximum cross section of the dam appears to be the primary contribution of ow into the seepage zone (spring) observed in Prole P6 (Figure 4) as well as in the eld. conductivity K = 3.7 105 m/s) of the soil sample. Substituting the value of the permeability into Equation 4, we obtain QV = 1.5 C/m3 . Using Equation 8, the effec- tive charge per unit volume is given by QV = C/ (K). Using this formula with the measured parameters given previously yields QV = 1.5 C/m3 . The two estimates are therefore very close to each other. The value of QV = 1.5 C/m3will be used to convert the source current density distribution into Darcy velocity. Using, however, a single value for QV while the dam is heterogeneous can only yield a rough estimate of the Darcy velocity. This will be discussed in the following section. Inverting the SP Field The SP data from Prole P6 were inverted to understand the seep observed in the eld at location A2 in Prole P6 (see Figure 4). We consider N = 55 SP stations along Prole P6 and we use M = 103 cells to discretize the subsurface as shown in Figure 10. The prior model m0 used for the inversion of the SP data is determined from a simulation of the groundwater ow assuming the position of the bedrock/aquifer inter- face (from the resistivity data) and a uniform permeability R2 = 0.98 Streaming potential coupling coefficient C = 2.6 0.2 mV m 1 0 0.2 0.4 0.6 0.8 1.0 Hydraulic head (m) Differenceofelectricalpotential(mV) 5 4 3 2 Water Ref V Porous samplePermeable membrane h (a) (b) Figure 9. Measurement of the streaming potential coupling coefcient for a core sample from the dam. (a) Sketch of the experimental setup where h denotes the hydraulic head. (b) The measurements have been made with water from the reservoir. The value of the streaming potential coupling coefcient is 2.6 0.2 mV/m. for the aquifer. We specify the boundary conditions for the head at the top and bottom of the prole and the ground- water ow is modeled in steady state. For the matrix Wd, we use a standard deviation of =3 mV from the data displayed in Figures 4 to 6. For the matrix W m, we use 2 m=100 to let enough freedom to the inverted model to depart from the prior model m0. A linear hydrostatic pressure head prole was com- puted and applied to the upstream slope to vary the hydraulic head applied to the model boundary based on relative elevation of the boundary with respect to the high pool water level. A seepage face was dened at the down- stream toe where seepage has been observed, as H = 0 m under saturated conditions and a specied ux equal to 0 m3 /s otherwise. All other model boundaries were given a specied ux equal to 0 m3 /s. For the electrical model, a current ow boundary was applied to the reservoir bed, upstream slope of the dam, and the downstream seepage face. The current densities at these boundaries were computed from the electrokinetic equations that couple the electric eld to the Darcy velocity computed in the hydraulic model. Modeling results are shown in Figure 10. The current density vector is translated into Darcy velocity using the linear relationship between current density and Darcy velocity (see Equation 3) u = jS/QV using QV = 1.5 C/m3. The results of the SPT are consistent with the position of the bedrock (for which the Darcy velocity should be very small). The two positive SP anomalies are explained by the convergence of the ow due to the fact that the bedrock is shallower in the vicinity of these anomalies. The seepage corresponding to the spring is shown very well by the inverted Darcy ow, showing a high Darcy velocity oriented partly upward at the position of the SP anomaly. A slug test performed in piezometer Pz1 indicates that the permeability of the formation is on the order of 1012 m2 (K = 105 m/s), which is a pretty large NGWA.org S. J. Ikard et al. Groundwater 11
  12. 12. Horizontal distance (m) 0 10 20 30 40 50 Ground surface Seepage Crest Bedrock Depth(m) 0 2 4 6 8 10 12 14 Darcy velocity from the self-potential data (P6) Aquifer Log10 (Darcy velocity, m/s) 5.5 5.0 4.5 4.0 3.5 Fit of the self-potential data 20 10 0 10 20(a) (b) Self-potential(inmV) Horizontal distance (m) Data Best fit 0 10 20 30 40 50 Pz1 Pz2 Figure 10. Result of the inversion of the SP data along Prole 6 and ow Path #2. (a) Best t of the experimental data at the third iteration of the Gauss-Newton algorithm. The standard deviation on the data is considered to be 3 mV from the scatter in the SP data. (b) Result of the Darcy velocity distribution assuming an excess of charge density of 1.5 C/m and the inverted source current density obtained at the third iteration. The dashed line represents approximately the interface between the bedrock and the aquifer determined from the resistivity data. The white area between the water table and the ground surface corresponds to the vadose zone. value. From the shape of the vadose zone shown in Figure 4, the head gradient is estimated to be on the order of 0.33. Therefore, the Darcy velocity is about 3 10-6 m/s in the vicinity of the piezometer Pz1. The SP tomogram converted into Darcy velocity distribution (Figure 10) indicates a higher Darcy velocity on the order of 3 105 m/s in this region so it is possible that the SP tomogram slightly overestimates the Darcy velocity possibly because of the value of QV chosen previously. Conclusions A small earthen dam exhibiting concentrated internal seepage and a visible seep at the toe was imaged using DC resistivity and SP during an instance of maximum reservoir capacity and therefore peak hydraulic loading. A series of 2D resistivity proles were inverted individually and combined for 3D inversion. SP data were collected along the resistivity proles for comparison. The SP data were inverted to estimate Darcy velocities. The following conclusions have been reached: 1. Resistivity identies three potential owpaths; how- ever, resistivity is not a direct indicator of permeability and uid ow. 2. SP can be directly tied to permeability and the source current density responsible for the SP signals is proportional to the Darcy velocity. However, the 12 S. J. Ikard et al. Groundwater NGWA.org
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Case Study/ Characterization of Focused Seepage Through an Earthfill Dam Using Geoelectrical Methods by S. J. Ikard 1 , A. Revil 2,3 , M. Schmutz 4 , M. Karaoulis 5 , A. Jardani 6 , and M. Mooney 7 Abstract Resistivity and self-potential tomography can be used to investigate anomalous seepage inside heterogeneous earthen dams. The self-potential (SP) signals provide a unique signature to groundwater flow because the source current density responsible for the SP signals is proportional to the Darcy velocity. The distribution of the SP signals is also influenced by the distribution of the resistivity; therefore, resistivity and SP need to be used in concert to elucidate groundwater flow pathways. In this study, a survey is conducted at a small earthen dam in Colorado where anomalous seepage is observed on the downstream face at the dam toe. The data reveal SP and direct current resistivity anomalies that are used to delineate three anomalous seepage zones within the dam and to estimate the source of the localized seepage discharge. The SP data are inverted in two dimensions using the resistivity distribution to determine the distribution of the Darcy velocity responsible for the observed seepage. The inverted Darcy velocity agrees with an estimation of the Darcy velocity from the hydraulic conductivity obtained from a slug test and the observed head gradient. Introduction Earthen dams are designed to allow a limited amount of uniform seepage through their cores and foundations. When seepage exceeds than what is permitted, internal erosion may occur and increase locally the permeability of preferential flowpaths. As the permeability is increased through erosion of finer particles, the hydraulics of seepage zones will also change over time. This can 1 Department of Geophysics, Colorado School of Mines, Green Center, Golden, CO; [email protected] 2 ISTerre, CNRS, UMR CNRS 5275, Universit´ e de Savoie, Le Bourget du Lac, France. 3 Corresponding author: Department of Geophysics, Colorado School of Mines, Green Center, Golden, CO; [email protected] 4 EA 4592, Institut Polytechnique de Bordeaux, 1 all´ ee Daguin, Pessac, France; [email protected] 5 Department of Geophysics, Colorado School of Mines, Green Center, Golden, CO. 6 Morphodynamique Continentale et oti` ere, M2C, UMR CNRS 6143, Universit´ e de Rouen, Mont Saint Aignan, France; [email protected] 7 Department of Civil & Environmental Engineering, Colorado School of Mines, Golden, CO, [email protected] Received June 2013, accepted November 2013. © 2013, National Ground Water Association. doi: 10.1111/gwat.12151 lead to the formation of piping through the dam and the development of subsurface voids, both of which can cause sinkholes on the crest or side-slopes (Fell et al. 2003; Bendahmane et al. 2008). The occurrence of such localized seepages zones may therefore result in the sudden failure of an earthen dam (Foster et al. 2002; Fell et al. 2003). These processes are responsible for the second cause of catastrophic failures for earthen dams, for about 46 % of all documented failures (Foster et al. 2000, 2002; Fell et al. 2003; Wan and Fell 2004). The highly uncertain outcomes and timescales over which seepage zones can evolve to threaten the safety condition of an earthen dam mandate a need for improved methodologies that allow for (1) noninvasive detection capabilities with improved resolution over broad and compact spatial scales, (2) rapid deployment and detection capabilities so that the geometrical evolution of seepage zones can be monitored in real time, and (3) the ability to provide quantitative estimates of seepage-related hydraulic parameters in real time with improved accuracy. Our goal in this study is to take advantage of some recent developments in self-potential tomography (SPT) (Soueid Ahmed et al. 2013), in order to detect preferential flowpaths in earthen dams. The self-potential (SP) method NGWA.org Groundwater 1
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